In [1]} Landau showed that a Feynman integral can have singularities only if certain polynomial equations are satisfied. In this section we review (largely following [2]}) the formulation of the Landau equations in momentum twistor space. A significant advantage of working in momentum twistor space is that some of the Landau equations (the on-shell conditions) can be solved analytically, in many non-trivial cases (such as the showcase of this paper: Fig. REF (b)), via simple geometric considerations (see for example [3]} for some simpler examples). We also review the equivalence of solutions to the Landau equations under certain graphical moves and the role of ziggurat graphs for classifying solutions of the Landau equations in massless planar theories.
